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# If 4<(7-x)/3, which of the following must be true?

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Re: If 4<(7-x)/3, which of the following must be true?  [#permalink]

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12 Feb 2018, 11:02
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If 4<(7-x)/3, which of the following must be true?

I. 5<x
II. |x+3|>2
III. -(x+5) is positive

(A) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III

Simplifying the given inequality we have:

4 < (7 - x)/3

12 < 7 - x

5 < -x

-5 > x

Since x is less than -5, we see that |x+3| > 2.

Also, since x < -5, we see that x + 5 will always be negative and thus -(x+5) will always be positive.

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If 4<(7-x)/3, which of the following must be true?  [#permalink]

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05 May 2018, 05:09
Bunuel wrote:
SOLUTION

If 4<(7-x)/3, which of the following must be true?

I. 5<x
II. |x+3|>2
III. -(x+5) is positive

(A) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III

Note that we are asked to determine which MUST be true, not could be true.

$$4<\frac{7-x}{3}$$ --> $$12<7-x$$ --> $$x<-5$$. So we know that $$x<-5$$, it's given as a fact. Now, taking this info we should find out which of the following inequalities will be true OR which of the following inequalities will be true for the range $$x<-5$$.

Basically the question asks: if $$x<-5$$ which of the following is true?

I. $$5<x$$ --> not true as $$x<-5$$.

II. $$|x+3|>2$$, this inequality holds true for 2 cases, (for 2 ranges): 1. when $$x+3>2$$, so when $$x>-1$$ or 2. when $$-x-3>2$$, so when $$x<-5$$. We are given that second range is true ($$x<-5$$), so this inequality holds true.

Or another way: ANY $$x$$ from the range $$x<-5$$ (-5.1, -6, -7, ...) will make $$|x+3|>2$$ true, so as $$x<-5$$, then $$|x+3|>2$$ is always true.

III. $$-(x+5)>0$$ --> $$x<-5$$ --> true.

Bunuel if the question asks: if $$x<-5$$ which of the following is true?

how can $$|x+3|>2$$, this inequality hold true for BOTH cases ?

you write "when $$x+3>2$$, so when $$x>-1$$ "

so if $$x>-1$$ how can it hold true when $$x<-5$$ So if $$x < -5$$ then $$x$$ can be -6, -7 -8 , -9 etc all negative numbers starting from -6 , whereas $$x>-1$$ means thar x can be 0, 1, 3, 4 etc all positive numbers

can you explain this part, please
Math Expert
Joined: 02 Sep 2009
Posts: 52431
Re: If 4<(7-x)/3, which of the following must be true?  [#permalink]

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05 May 2018, 10:00
1
dave13 wrote:
Bunuel wrote:
SOLUTION

If 4<(7-x)/3, which of the following must be true?

I. 5<x
II. |x+3|>2
III. -(x+5) is positive

(A) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III

Note that we are asked to determine which MUST be true, not could be true.

$$4<\frac{7-x}{3}$$ --> $$12<7-x$$ --> $$x<-5$$. So we know that $$x<-5$$, it's given as a fact. Now, taking this info we should find out which of the following inequalities will be true OR which of the following inequalities will be true for the range $$x<-5$$.

Basically the question asks: if $$x<-5$$ which of the following is true?

I. $$5<x$$ --> not true as $$x<-5$$.

II. $$|x+3|>2$$, this inequality holds true for 2 cases, (for 2 ranges): 1. when $$x+3>2$$, so when $$x>-1$$ or 2. when $$-x-3>2$$, so when $$x<-5$$. We are given that second range is true ($$x<-5$$), so this inequality holds true.

Or another way: ANY $$x$$ from the range $$x<-5$$ (-5.1, -6, -7, ...) will make $$|x+3|>2$$ true, so as $$x<-5$$, then $$|x+3|>2$$ is always true.

III. $$-(x+5)>0$$ --> $$x<-5$$ --> true.

Bunuel if the question asks: if $$x<-5$$ which of the following is true?

how can $$|x+3|>2$$, this inequality hold true for BOTH cases ?

you write "when $$x+3>2$$, so when $$x>-1$$ "

so if $$x>-1$$ how can it hold true when $$x<-5$$ So if $$x < -5$$ then $$x$$ can be -6, -7 -8 , -9 etc all negative numbers starting from -6 , whereas $$x>-1$$ means thar x can be 0, 1, 3, 4 etc all positive numbers

can you explain this part, please

I tried to explain this here: https://gmatclub.com/forum/if-4-7-x-3-w ... l#p1465124 and here: https://gmatclub.com/forum/if-4-7-x-3-w ... l#p1991132

For more on this kind of questions check Trickiest Inequality Questions Type: Confusing Ranges (part of our Special Questions Directory).
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Re: If 4<(7-x)/3, which of the following must be true?  [#permalink]

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05 Aug 2018, 04:05
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If 4<(7-x)/3, which of the following must be true?

I. 5<x
II. |x+3|>2
III. -(x+5) is positive

(A) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III

Problem Solving
Question: 156
Category: Algebra Inequalities
Page: 82
Difficulty: 600

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4<(7-x)/3
i)5<x which isn't true
ii) x<-5
x+3<-2 hence |x+3|>2
choice ii is correct
iii)x<-5
x+5<0
-(x+5)>0
choice iii is correct
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Re: If 4<(7-x)/3, which of the following must be true? &nbs [#permalink] 05 Aug 2018, 04:05

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